{
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  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='svg'\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt  # Plotting library\n",
    "from matplotlib.colors import colorConverter, ListedColormap\n",
    "from mpl_toolkits.mplot3d import Axes3D  # 3D plots\n",
    "from matplotlib import cm # Colormaps\n",
    "import seaborn as sns  # Fancier plots\n",
    "\n",
    "# Set matplotlib and seaborn plotting style\n",
    "sns.set_style('darkgrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "def logistic(z: np.ndarray) -> np.ndarray:\n",
    "    \"\"\"logistic function\"\"\"\n",
    "    return 1. / (1 + np.exp(-z))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
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  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
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   "source": [
    "z = np.linspace(-8, 8, 100)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(5, 3))\n",
    "ax.plot(z, logistic(z), 'b-')\n",
    "ax.set_xlabel('$z$', fontsize=12)\n",
    "ax.set_ylabel('$\\sigma(z)$', fontsize=12)\n",
    "ax.set_title('logistic function')\n",
    "ax.set_xlim(-8, 8)\n",
    "plt.show()"
   ],
   "metadata": {
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    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "def logistic_derivative(z: np.ndarray) -> np.ndarray:\n",
    "    return logistic(z) * (1. - logistic(z))"
   ],
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    "pycharm": {
     "name": "#%%\n"
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  {
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    {
     "data": {
      "text/plain": "(-8.0, 8.0)"
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     "execution_count": 5,
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   "source": [
    "z = np.linspace(-8, 8, 100)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(5, 3))\n",
    "ax.plot(z, logistic_derivative(z), 'r-')\n",
    "ax.set_xlabel('$z$', fontsize=12)\n",
    "ax.set_ylabel('$\\\\frac{\\\\partial \\\\sigma(z)}{\\\\partial z}$', fontsize=12)\n",
    "ax.set_title('derivative of the logistic function')\n",
    "ax.set_xlim(-8, 8)"
   ],
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    "pycharm": {
     "name": "#%%\n"
    }
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  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [],
   "source": [
    "def softmax(z):\n",
    "    \"\"\"Softmax function\"\"\"\n",
    "    return np.exp(z) / np.sum(np.exp(z))"
   ],
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    "collapsed": false,
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     "name": "#%%\n"
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   "cell_type": "code",
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Min\\AppData\\Local\\Temp\\ipykernel_2296\\2795926633.py:20: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
      "  cbar = fig.colorbar(surf)\n"
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   ],
   "source": [
    "# Plot the softmax output for 2 dimensions for both classes\n",
    "# Plot the output in function of the weights\n",
    "# Define a vector of weights for which we want to plot the output\n",
    "nb_of_zs = 33\n",
    "zs = np.linspace(-10, 10, num=nb_of_zs) # input\n",
    "zs_1, zs_2 = np.meshgrid(zs, zs) # generate grid\n",
    "y = np.zeros((nb_of_zs, nb_of_zs, 2)) # initialize output\n",
    "# Fill the output matrix for each combination of input z's\n",
    "for i in range(nb_of_zs):\n",
    "    for j in range(nb_of_zs):\n",
    "        y[i,j,:] = softmax(np.asarray([zs_1[i,j], zs_2[i,j]]))\n",
    "# Plot the loss function surfaces for both classes\n",
    "with sns.axes_style(\"whitegrid\"):\n",
    "    fig = plt.figure(figsize=(6, 4))\n",
    "    ax = fig.add_subplot(1, 1, 1, projection='3d')\n",
    "    # Plot the loss function surface for t=1\n",
    "    surf = ax.plot_surface(zs_1, zs_2, y[:,:,0], linewidth=0, cmap=cm.magma)\n",
    "    ax.view_init(elev=30, azim=70)\n",
    "    ax.grid(False)\n",
    "    cbar = fig.colorbar(surf)\n",
    "    ax.set_xlabel('$z_1$', fontsize=2)\n",
    "    ax.set_ylabel('$z_2$', fontsize=12)\n",
    "    ax.set_zlabel('$y_1$', fontsize=12)\n",
    "    ax.set_title ('$P(t=1|\\mathbf{z})$')\n",
    "    cbar.ax.set_ylabel('$P(t=1|\\mathbf{z})$', fontsize=12)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The watermark extension is already loaded. To reload it, use:\n",
      "  %reload_ext watermark\n",
      "Last updated: 2022-07-12T17:05:12.015382+08:00\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.10.4\n",
      "IPython version      : 8.4.0\n",
      "\n",
      "Compiler    : MSC v.1916 64 bit (AMD64)\n",
      "OS          : Windows\n",
      "Release     : 10\n",
      "Machine     : AMD64\n",
      "Processor   : AMD64 Family 23 Model 96 Stepping 1, AuthenticAMD\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "numpy     : 1.22.3\n",
      "matplotlib: 3.5.1\n",
      "sys       : 3.10.4 | packaged by conda-forge | (main, Mar 30 2022, 08:38:02) [MSC v.1916 64 bit (AMD64)]\n",
      "seaborn   : 0.11.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark\n",
    "%watermark --iversions"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
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